Question 241983
A general form for sin and cos functions is:
y = C + A*sin(B(x - D))
or
y = C + A*cos(B(x - D))
where
{{{abs(A)}}} = Amplitude. So A = 2 or -2.
B = {{{2pi}}}/period
C = Vertical shift
D = Horizontal (or phase) shift<br>
You are given the amplitude so you know A. You are given the period so we can figure out B:
{{{B = (2pi)/(pi/4)}}}
{{{B = 8}}}
You are not given a vertical shift so we will use 0 for C. And you are give the phase shift so D = {{{pi/2}}}.<br>
So now we just find the equation that fits the A, B, C and D the we found above. It should be clear that equation (a) is correct.<br>
(BTW: The -2 for A means that the amplitude is 2 and, because of the minus, the graph is reflected about the x-axis.)